Contents

Preface

Chapter 1

Binary Collision of Structureless Particles

1.1. Dynamics of Collision of Two Particles

1.2. Effective Scattering Cross-Section. Relationships between Relative Velocities

Chapter 2

Levels and Stages of Modeling. Classic Equations of Kinetics and Hydrodynamics

2.1. Transition to Statistical Level from Dynamic Level of Medium Modeling. Bogolyubov-Born-Green-Kirkwood-Yvon Hierarchy of Equations

2.2. Kinetic Stage of Modeling. Equations for One-Particle Distribution Function

2.3. Factorized Solutions to Equations of BBGKY Hierarchy

2.4. Bogolyubov Boundary Condition for Correlations Failure and Boltzmann Hypothesis of Molecular Chaos

2.5. Properties of Boltzmann Equation and Boltzmann Collision Integral. Moments of One-Particle Distribution Function and Equations for Moments

2.6. Passage to Hydrodynamic Stage of Modeling. Equations of Classic Hydrodynamics

Chapter 3

Equation for Pair of Particles at Initial Stage of Modeling

3.1. Physical Meaning of Error Introduced by Boltzmann Hypothesis into Classic Hydrodynamics

3.2. Concept of Pair of Particles. Heuristic Derivation of Equation for Pair of Particles

3.3. Multi-Scale Method of Derivation of Equation for Pair of Particles

3.4. Conditional Probabilities Method of Derivation of Equation for Pair of Particles

Chapter 4

Equations for Pair and Paired-Particle Distribution Functions at Hydrodynamic Stage of Modeling

4.1. Pair and Paired-Particle Distribution Functions. Relationships between Distribution Functions

4.2. Equations for Pair Distribution Functions. Hydrodynamic Stage of Modeling

4.3. Heuristic Derivation of Equations for Pair Distribution Functions. Basic Property of Pair Distribution Functions

4.4. Equations for Paired-Particle Distribution Functions. Hydrodynamic Stage of Modeling

4.5. Relationships between One-Particle and Pair Distribution Functions

Chapter 5

Derivation of Equations of Multimoment Hydrodynamics

5.1. Definition of Hydrodynamic Values in Terms of Pair Distribution Functions. Principle Hydrodynamic Values

5.2. Transition from Equations for Pair and Paired-Particle Distribution Functions to Hydrodynamics Equations

5.3. Grad Expansion of Pair Distribution Function

5.4. Calculation of Collision Integrals

5.5. Transformation of Equations of Multimoment Hydrodynamics

5.6. Ultimate Set of Equations of Multimoment Hydrodynamics

Chapter 6

Pair and One-Particle Entropy of System

6.1. Expressions for Pair and One-Particle Entropy of System in Terms of Principle Hydrodynamic Values

6.2. Pair and One-Particle Entropy Production in Collisions. Temporal and Spatial Variation of Pair and One-Particle Entropy

6.3. Equations of Multimoment Hydrodynamics in Limit of Weak Non-Equilibrium

6.4. One-Particle Entropy Production in Limit of Weak Non-Equilibrium. Specification of Characteristic Time between Collisions

Chapter 7

Emergence of Irreversibility in Ultimate Equations

7.1. Problem on Emergence of Irreversibility

7.2. Transition of Information about Direction of Evolution from Initial Conditions to Ultimate Equations

7.3. Irreversible Replacing and Boltzmann Hypothesis of Molecular Chaos

7.4. Reverse Equations of Multimoment Hydrodynamics

7.5. Usually Observed and Extremely Unlike Direction of Evolution

References

About the Author

Index

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